Bill O’Reilly’s position at Fox News grew increasingly tenuous on Tuesday as support from the Murdoch family showed signs of eroding, according to three people briefed on discussions about his future.

Mr. O’Reilly’s fate at the network is expected to be discussed on Thursday at a board meeting for Fox News’s parent company, 21st Century Fox. Chief among the considerations is a continuing investigation into Mr. O’Reilly’s behavior conducted by the law firm Paul, Weiss, Rifkind, Wharton & Garrison.

Pressure on the company increased on Tuesday when another woman reported sexual harassment allegations against Mr. O’Reilly to 21st Century Fox.

The company recently renewed Mr. O’Reilly’s contract, and the Murdoch family, which controls the company, has stood by him as allegations piled up. But after a New York Times article this month detailed harassment allegations against him, more than 50 companies have pulled their advertising from his show.

Women inside the company have questioned whether the company was serious about fixing a workplace culture beset by repeated allegations of sexual harassment. And calls for his dismissal grew louder Tuesday.

Mr. O’Reilly, the top-rated host in cable news, has been on vacation in Italy for the past week and plans to return to his show on Monday. He has received no indication that the company is planning to take him off the air, according to a person familiar with the matter.

A lawyer for Mr. O’Reilly, Marc E. Kasowitz of Kasowitz Benson Torres, said Tuesday that his client was being targeted by liberal groups trying to bring him down. “Bill O’Reilly has been subjected to a brutal campaign of character assassination that is unprecedented in post-McCarthyist America,” he said in a statement. “This law firm has uncovered evidence that the smear campaign is being orchestrated by far-left organizations bent on destroying O’Reilly for political and financial reasons. That evidence will be put forth shortly, and it is irrefutable.”

A decision on Mr. O’Reilly’s future could come in the next few days.

If he is forced to depart, it would be a major blow to the network, which in the past year has also lost its founding chairman, Roger E. Ailes, and another prime-time star, Megyn Kelly. It would also be a stunning downfall for Mr. O’Reilly, who has dominated the prime-time cable news landscape for most of two decades with a pugnacious, anti-political-correctness commentary that appeals to conservative viewers.

The latest allegation against Mr. O’Reilly came on Tuesday when a woman who previously worked at Fox News called a 21st Century Fox hotline to report allegations of sexual and racial harassment against him, according to her lawyer, Lisa Bloom. The woman, who is not seeking money, wanted to stay anonymous to avoid the news media spotlight but thought that it was important to report her allegations to the company, Ms. Bloom said.

Ms. Bloom said the woman, who is African-American, worked in a clerical position at the network but did not work directly for Mr. O’Reilly. The woman reported that in 2008, Mr. O’Reilly would stop by her desk and grunt like a “wild boar”; he would also stand back to allow her to exit the elevator first and then say, “Looking good, girl,” Ms. Bloom said. Mr. O’Reilly leered at the woman’s cleavage and legs and called her “hot chocolate,” Ms. Bloom said.

Ms. Bloom said she had talked to the woman’s sister as well as her roommate and boyfriend at the time, who all said the woman had told them of the allegations. The investigation by Paul Weiss was expected to expand if other problems involving Mr. O’Reilly were reported.

“She just felt like she had to do the right thing and include her story,” Ms. Bloom said.

Mr. Kasowitz responded strongly to the allegation, saying there was reason to be skeptical of the woman’s claim.

“It is outrageous that an allegation from an anonymous person about something that purportedly happened almost a decade ago is being treated as fact, especially where there is obviously an orchestrated campaign by activists and lawyers to destroy Mr. O’Reilly and enrich themselves through publicity-driven donation,” Mr. Kasowitz said.

Although Mr. O’Reilly, 67, brings immense value to 21st Century Fox as a ratings draw and a revenue generator, the Murdoch family will have to weigh those considerations against its other ambitions. Those include overhauling a Fox News culture that has been damaged by repeated sexual harassment allegations and pursuing the acquisition of the British satellite company Sky, long coveted by the family patriarch, Rupert Murdoch. The company must convince British regulators next month that it is fit to acquire the 61 percent in Sky that it does not own.

Questions about Mr. O’Reilly’s future come just weeks after The Times reported that Mr. O’Reilly or the company had made payouts to five women involving allegations of inappropriate behavior by Mr. O’Reilly. In exchange, the women agreed not to sue or speak of the allegations. The payouts totaled about $13 million.

Two of the deals were struck by 21st Century Fox last year after Mr. Ailes was pushed out following accusations by several women of sexual harassment. In the aftermath of Mr. Ailes’s dismissal, the company said behavior that “disrespects women or contributes to an uncomfortable work environment” would not be tolerated. The Times reported that two other women — who had not received payouts — had accused Mr. O’Reilly of harassing them. One of those women has since reported her accusations to 21st Century Fox.

Mr. O’Reilly and Mr. Ailes have denied the allegations against them.

New York magazine reported earlier Tuesday that the Murdochs were leaning toward announcing that Mr. O’Reilly would not return to his show.

Over the past two weeks, protests against 21st Century Fox, Fox News and Mr. O’Reilly have intensified. After a series of online campaigns urged advertisers to pull their spots from his show, advocacy groups organized protests outside the Fox News headquarters.

On Tuesday, the women’s advocacy group UltraViolet led a rally of sexual assault survivors outside the Fox News headquarters in Manhattan, calling for the ouster of Mr. O’Reilly. The group also commissioned an airplane to fly over New York City with a banner that read, “Fox: #DropOReilly, The Sexual Predator.”

The group directly targeted James Murdoch, the chief executive of 21st Century Fox, who has pushed to modernize the company’s workplace. UltraViolet sent a letter to him signed by more than 450 people described as victims of sexual harassment that read in part: “The lurid details of Mr. O’Reilly’s crimes, and Fox News’ role in protecting him while systematically destroying the women he has victimized, are disturbing yet completely unsurprising. We know firsthand that survivors of sexual crimes are silenced, shamed, and vilified by perpetrators and onlookers, and 21st Century Fox has gone as far as to protect O’Reilly from his accusers with monetary payouts.”

Despite the exodus of advertisers, Mr. O’Reilly’s show has maintained strong ratings.

Mr. O’Reilly in recent days has ratcheted up the rebuttal to the women’s accusations. In response to questions last week about how Fox News’s support for him was a factor in Ms. Kelly’s departure from the network, Mr. O’Reilly’s lawyer said in a statement that it had become “apparent to any objective observer that Mr. O’Reilly is being subjected to a malicious campaign intent on harming his reputation and family through speculation and innuendo.”

An ominous sign for Mr. O’Reilly came Thursday from Matt Drudge, who is known to have close connections to people within Fox News. “O’Reilly has had tremendous run,” he said in a Twitter post. “Very few in the business get to decide when and how things end. Media is most brutal of all industries…”

Fox News will no longer even respond to questions about whether Bill O'Reilly will return to his show.

A well-placed source said Tuesday afternoon that representatives for Fox and O'Reilly have begun talking about an exit. But this prompted a denial from sources in O'Reilly's camp.

Even one person close to O'Reilly, however, said he will probably not be back on "The O'Reilly Factor."

The original well-placed source said an announcement about O'Reilly's fate was likely by the end of the week.

The fact that none of these sources were willing to go on the record speaks to the delicate maneuvering underway.The network's parent company, 21st Century Fox (FOX), will hold a board meeting on Thursday, a spokeswoman told CNNMoney. One of the sources said O'Reilly will be a primary topic.

The Murdochs, the men who control 21st Century Fox, are pointedly not commenting on any of this.

New York magazine's Gabriel Sherman, the author of a biography about ex-Fox News boss Roger Ailes, reported Tuesday that "the Murdochs are leaning toward announcing that O'Reilly will not return to the air."

Sherman cited "three sources with knowledge of the discussions" and said "no final decision has been made."

As CNNMoney has previously reported, there had been a split between Rupert Murdoch, the company's patriarch, and his sons James and Lachlan, with James advocating for O'Reilly's ouster. Lachlan was previously said to be in the middle. Sherman said Tuesday that Lachlan has "leaned more in his brother James's direction" in recent days.All of this is a reaction to a New York Times story about the settlement payments that O'Reilly, Fox and 21st Century Fox paid to women who accused O'Reilly of sexual harassment and verbal

Last week 21st Century Fox confirmed that an outside law firm was investigating allegations against O'Reilly.The same firm -- Paul, Weiss -- played an instrumental role in the eventual resignation of Ailes last summer.O'Reilly's allies feel that he has been unfairly demonized by his accusers and a biased news media.

His opponents, including some influential voices inside 21st Century Fox, feel that O'Reilly has behaved badly over the years, that his behavior has been exposed, and that it's inappropriate for Fox News to continue his show.

"The O'Reilly Factor" is by far the highest-rated program on cable news. But most of O'Reilly's advertisers abandoned the show in the wake of the Times' story.

O'Reilly began a pre-planned vacation to Italy last week. When he announced the vacation on air, Fox News and O'Reilly's own outside spokesman said he'd be back on the "Factor" on April 24. Guest hosts are filling in this week.

O'Reilly remains in Italy while his team of agents and lawyers in New York work on his behalf.

Some sources on O'Reilly's side said that, as of Tuesday afternoon, they still expect he'll be back on "The O'Reilly Factor" on Monday.

But they acknowledged that none of them know for sure.

Fox recently renewed O'Reilly's contract with the knowledge that the Times' story was in the works.

The Times reported that the new deal was structured to give Fox "more leverage over him regarding his behavior."That could be a factor in negotiations now.

If O'Reilly does resign, or if Fox takes him off the air, he'd be the third major player to leave the network in the span of nine months. Ailes' resignation last July was the result of sexual harassment charges by women at the network, including Megyn Kelly, who herself left Fox in January. O'Reilly defended Ailes when the women first came forward.

Kelly decided to leave Fox News in January. She is launching two new shows on NBC later this year.

Fox's audience has remained extraordinarily loyal to the network amid all of the off-air controversies.

And many of O'Reilly's fans are waiting for him to get back from vacation.

But on Tuesday, Fox would no longer confirm his April 24 return date.

When asked, "Will O'Reilly be returning to the Factor on April 24?," the Murdochs' top spokesperson did not respond.